Half-space theorems for recurrent minimal and -surfaces of

  • G. Pacelli Bessa

    Universidade Federal do Ceará, Fortaleza-Ceará, Brazil
  • Luquesio P. Jorge

    Universidade Federal do Ceará, Fortaleza-Ceará, Brazil
  • Leandro F. Pessoa

    Universidade Federal do Piauí, Teresina-Piauí, Brazil
Half-space theorems for recurrent minimal and $H$-surfaces of $\mathbb{R}^{3}$ cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

We prove a version of the strong half-space theorem between the classes of recurrent minimal surfaces and complete minimal surfaces with bounded curvature of . The use of subsolutions in the barrier sense allow us to deal with non-proper minimal surfaces immersed with bounded curvature. We show that any minimal hypersurface immersed with bounded curvature in equals some provided is a complete, recurrent -dimensional Riemannian manifold with and whose sectional curvatures are bounded from above. Furthermore, we prove a half-space theorem for the class of stochastically complete -surfaces. We present a maximum principle at infinity assuming has non-empty boundary. Finally, we present examples of a complete non-proper recurrent minimal surface with unbounded curvature.

Cite this article

G. Pacelli Bessa, Luquesio P. Jorge, Leandro F. Pessoa, Half-space theorems for recurrent minimal and -surfaces of . Rev. Mat. Iberoam. 40 (2024), no. 5, pp. 1609–1630

DOI 10.4171/RMI/1498